Math III, Unit 4, Lesson 1 - Ciclt.net

Acquisition Lesson Planning FormPlan for the Concept, Topic, or Skill – Applying the Properties of Logarithms and Exponential FunctionsKey Standards addressed in this Lesson: MM3A2d,gTime allotted for this Lesson:Standard: MM3A2d,g: Students will explore logarithmic functions as inverses of exponentialfunctions.d. Understand and use properties of logarithms by extending laws of exponents.g. Explore real phenomena related to exponential and logarithmic functions including half – lifeand doubling life.Essential Question: How do properties of logarithms and laws of exponents relate to real phenomena?Activating Strategies:Give your students a list of log and exponential problems to simplify for review.5 log 5 3 log 4 8 4 √2 *4 √2 log 6 6 2 (x √3 ) √3Acceleration/Previewing: (Key Vocabulary)Logarithms, exponents, half – life, appreciation, depreciation, common logarithm, exponential functions,logarithmic functionsTeaching Strategies:Use the folding activity, Paper folding with Exponential and Logarithmic Functions, to help reinforce theconcept that logs and exponential functions are inverse functions.Use Graphic Organizer to demonstrate how to solve exponential equations.Demonstrate how to use the properties of logs to solve log equations.Use the Graphic Organizer (flowers) to introduce the real phenomena equations for solving equationsinvolving logs and exponentials.Work a few problems together as a class.Task:Investigating the Properties of LogarithmsPotato LabHistorical BackgroundDistributed Guided Practice:Exponential Real Word Problems Worksheet (individually or in pairs)Can find extra worksheets at www.kutasoftware.comExtending/Refining Strategies:Potato Lab TaskSummarizing Strategies:Journal: How are logarithmic and exponential functions relate? How do you solve logarithmic andexponential functions?

Exponential Real World ProblemsName: __________________________Date: _______________1. Joan invested $1000 3 years ago. It is now worth $1276. If interest iscompounded continuously, what is the interest rate?2. For a certain strain of bacteria, k is .775 when t is measured in hours.How long will it take 2 bacteria to increase to 1000?3. Dave bought a car 8 years ago for $5400. To buy a similar car todaywould cost $12,500. Assuming a steady rate of increase, what was theyearly rate of inflation?4. Jack deposited $100 in an account that pays 6% interest compoundedcontinuously. When he withdrew the money, there was a balance of $200.How long ago did he open the account?5. A strain of bacteria can grow from 3 to 15 in 3 hours. What is the valueof k?6. A $50 baseball card is worth $400 in 5 year time. What is the rate ofappreciation?7. How much will $500 earn if invested for 6% compounded continuouslyfor 5 years.8. In 5 years, the mass of a 100 gram sample of an element is reduced to 75grams. Find the value of k?`